Решите систему: [latex] left { {{|x-1|+|y-5|=1} atop {y=5+|x-1|}} ight. [/latex]

[latex] left { {{|x-1|+|y-5|=1} atop {y=5+|x-1|}} ight. \ |x-1|=y-5 \ y-5+|y-5|=1 \ left { {{y-5+y-5=1, y geq 5} atop {{y-5+5-y=1, y< 5}} ight. \ left { {{2y=11, y geq 5} atop {{0 eq 1, y< 5}} ight. \ y=5,5 \ y=5+|x-1| \ 5.5=5+|x-1| \ |x-1|=0.5 \ left { {{x-1=0.5} atop {x-1=-0.5}} ight. \ x_1=1.5 \ x_2=0.5[/latex]Ответ: (1,5; 5,5); (0,5; 5,5)